How can I remove a rusted nut and bolt?

You can use what's known as liquid wrench, better known as a cutting torch...LOL

Best thing is WD40 or some other liquid rust remover and after putting it on, bank on the bolts to help get it into the threads.

A product called PB Blaster works better than anything else I have used (including Liquid Wrench and much better than WD-40). Available at most auto parts stores.

If that won't cut it, you might need to find a nut splitter and break the nut or use a hacksaw to cut through the bolt.

Well if you want to remove the bolts and re-use them, try rust off which you can get at any hardware shop. But if you just want to remove it completely use an Angle Grinder with a metal cutting wheel.

If they can be heated without burning down the house then heat the nut to red hot and then throw cold water on them. Remove. If not grind the nut off the bolt and start over.

If a nut and bolt is rusted together, it's often easier to just cut it off. Use a manuel or power hacksaw, cutting disc, or a torch.

Try WD-40, or a pair of high pressure pliers (ex. Robogrips), or a Sawzall, if you have one.

WD-40 or a dremel tool ~

Hammer and chisel could work too.

they also make a nut splitter if you dont own a grinder...